I can evaluate the integrals. Could someone please check whether I've changed the order correctly?

1) $\displaystyle \int_0^1\int_{y^2}^1 2\sqrt{x}e^{x^2} \ dx \ dy$

= $\displaystyle \int_0^1\int_0^{\sqrt{x}} 2\sqrt{x}e^{x^2} \ dy \ dx$

2) $\displaystyle \int_0^1\int_{y}^1 e^{x^2} \ dx \ dy$

= $\displaystyle \int_0^1\int_{0}^x e^{x^2} \ dy \ dx$